Impact of the Reference Multiple-Time-Point Dosimetry Protocol on the Validity of Single-Time-Point Dosimetry for [177Lu]Lu-PSMA-I&T Therapy

Visual Abstract

Tar geting of the prostate-specific membrane antigen (PSMA) with [ 177 Lu]Lu-PSMA therapy evolved as a promising strategy for the treatment of metastasized castration-resistant prostate cancer, which is one of the main worldwide causes of death in men (1).The VISION trial led to the approval of [ 177 Lu]Lu-vipivotide tetraxetan (Pluvicto; Novartis) by the U.S. Food and Drug Administration in March 2022 and by the European Medicines Agency in December 2022 (2).Patient-specific internal dosimetry supports safe and efficient patient management during radionuclide therapy by monitoring the absorbed radiation dose to both healthy and malignant tissues (3,4).However, internal dosimetry requires quantitative images, preferably SPECT or PET, at multiple time points (MTPs) at least over the initial days after injection (5)(6)(7).The associated high number of examinations poses a high workload and additional costs to the clinics in cases of unclear reimbursement.These factors have so far limited the routine implementation of clinical dosimetry, although it is more and more legally requested (8,9).The rising number of therapies as expected after the U.S. Food and Drug Administration and European Medicines Agency approval of [ 177 Lu]Lu-vipivotide tetraxetan will probably further complicate the integration of routine dosimetry into the clinical workflow.On the other hand, only routine dosimetry with reasonable accuracy can provide the empiric knowledge that is necessary to tailor PSMA therapy more to the individual patient characteristics, as for example, with respect to treatment activity per cycle or number of cycles.
To handle the workload associated with increasing routine use of dosimetry, dosimetry based on fewer image acquisitions and even single-time-point (STP) dosimetry methods are being intensively investigated for 177 Lu-based treatments (10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25).Depending on the selected imaging time point, these protocols lay within an acceptable agreement of around 10% compared with a selected ground truth protocol that is based on serial quantitative imaging.To derive the time-integrated activity (TIA) for each tissue of interest, most of the proposed STP methods measure the uptake per tissue based on a single quantitative image and combine this single uptake measurement with some prior knowledge about the tissue-specific effective half-life.The latter could be a populationbased effective half-life or the patient-specific effective half-life of a former therapy cycle.Besides the exact STP method used for the calculation of the TIA itself, so far published methods differ regarding the considered reference model (Table 1).The reference model for MTP dosimetry is defined by the number and timing of the image acquisition itself and the mathematic fit model that is applied to the data points.These reference protocols are highly variable between institutions, as internal dosimetry still lacks standardization, and as site-specific protocols must be tailored to the local situation.Because the reference model is usually already limited by clinical feasibility, it cannot be considered a real ground truth but already represents an approximation with some protocol-dependent error.Thus, findings on STP dosimetry such as optimum time point and percentage deviation compared with MTP dosimetry cannot necessarily be transferred from one considered MTP reference protocol to another.The aim of this study was to investigate how the choice of reference model affects selection of the optimum method for STP dosimetry in the scope of [ 177 Lu]Lu-PSMA-I&T therapy.

Patients
This study included 7 patients diagnosed with metastasized castrationresistant prostate cancer in their first cycle of [ 177 Lu]Lu-PSMA-I&T therapy (Table 2).All patients gave written consent to undergo radiopharmaceutical therapy.The institutional review board approved this retrospective study, and the requirement to obtain informed consent was waived (reference 22-0552).

Dosimetry
Sixty lesions, 14 kidneys, and 10 submandibular glands were delineated daywise in the SPECT/CT data.Kidney volumes of interest (VOIs) were drawn manually on the CT data.Lesions and submandibular glands were delineated using a 30% isocontour of the average within a spheric VOI of 12-mm diameter centered at the tissue maximum (26,27).To allow for a more robust quantification, only lesions with volumes larger than 5 cm 3 were included.Only 10 submandibular glands could be investigated since segmentation was not possible for 2 patients because the field of view was too small.The parotid glands could not be evaluated, as they were not completely covered in the SPECT acquisitions.Mean activity concentrations and volumes were extracted.Absorbed doses were estimated using an in-house routine and mass-scaled organ and tumor S values as extracted from OLINDA/EXM version 2.0 (lesions: 2.33e205 Gy/[MBq 3 s], 1 g; kidneys: 7.74e208 Gy/[MBq 3 s], 310 g; salivary glands: 2.76e207 Gy/[MBq 3 s], 85 g) (28).

Reference MTP Dosimetry
The TIA was first estimated for each compartment by fitting and integrating all available imaging time points using a monoexponential model and a biexponential model.For the latter, all possible realizations with up to 3 free parameters as proposed by Hardiansyah et al. were considered (29).All fit functions were evaluated by common goodness-of-fit criteria, that is, the coefficients of variation (CV) and the sum of squared errors (30,31).Finally, the following 2 functions were used to fit the reference MTP model: f bi1, sg ðtÞ5A 0 ge 2ðlbio1lphysÞt 1A 0 ð12gÞe 2ðlphysÞt with shared g: A 0 refers to A(t 5 0), and l bio and l phys are the biologic and physical clearance rates, respectively.The population-based g-parameter modulates the transition from the phase with biologic clearance to the phase without biologic clearance and was determined by the jackknife method.For the latter, the respective function is fitted to the data of all patients except the one currently being investigated.The CV refer to the 2 free parameters A 0 (CV A ) and l bio (CV l ).

STP Dosimetry
Three different STP approaches were evaluated with a single SPECT/CT acquisition at 24, 48, 72, or 168 h after injection: a monoexponential (STP mono ) or a biexponential (STP bi ) function with populationbased biologic clearance rates; the method by H€ anscheid et al., originally established for 177 Lu-DOTATE/DOTATOC therapy (STP H ) (12); and the method proposed by Jackson et al. (STP J ) (11).
The TIA for STP mono is given by t SPECT and Aðt SPECT Þ refer to imaging time point and the VOI activity measured for that time point, respectively.Two population-based parameters, l bio and g, were used for STP bi , with the TIA being given by For STP H , the TIA is estimated by Á t SPECT : H€ anscheid et al. stated that if imaging is performed between 0:75 t 1=2, eff and 2:5 t 1=2, eff (t 1=2, eff is effective half-life), the error in the TIA is less than 10% (12).In this study, we investigated all available time points, assuming that time points that do not fulfil this criterion will automatically show a larger deviation from the reference.More information about the VOIs and time points t SPECT for which the criterion 0:75 t 1=2, eff , t SPECT , 2:5 t 1=2, eff was applied is given in Supplemental Table 2.
For STP J , it is assumed that with f tissue being a scaling factor depending on time point and compartment.The factors were recalculated for our patient cohort according to the method described by Jackson et al. because of the different PSMA compound used in this study (Supplemental Table 2) (11).

Data Evaluation
The Wilcoxon signed-rank test was used to compare the dosimetry estimates and the goodness-of-fit parameters for the reference models monoexponential MTP (MTP mono ) and biexponential MTP (MTP bi ).
Mean absolute deviations of STP methods from MTP mono and MTP bi were determined per compartment, whereupon STP mono was compared only with MTP mono and STP bi only with MTP bi .The best imaging time point or STP method was defined as the one with the lowest mean absolute deviation.The percentage of VOIs with a deviation of less than |10|% was used as a secondary criterion.

RESULTS
Table 3 shows the goodness-of-fit parameters for both the monoand biexponential reference model, as well as the statistical evaluation.For the salivary glands, MTP bi seemed to be superior to MTP mono , as both the CV and the sum of squared errors were significantly lower (P , 0.05).Such was not the case for the kidneys.The average goodness-of-fit parameters would favor MTP bi but without statistical significance (P .0.05).For the lesions, CV l bio significantly favored MTP mono (P , 0.05), whereas the sum of squared errors significantly favored MTP bi (P , 0.05).However, the monoexponential reference model yielded significantly lower absorbed doses than did the biexponential fit (Table 3).Although for both the kidneys and the lesions, no reference model was deemed to be superior, maximum absorbed dose deviations of 219% and 244% were found for kidneys and lesions, respectively (Table 3).As expected, CV l bio was found to be larger for lesions than for kidneys and salivary glands, indicating a larger pharmacokinetic variability for lesions.Average (6SD) effective half-lives were found to be 56.5 6 18.8, 32.9 6 5.9, and 22.5 6 2.8 h for lesions, kidneys, and salivary glands, respectively.More information on the distribution of effective half-lives and some exemplary time-activity curves are shown in Supplemental Figures 3-5.
The deviations of all STP methods and imaging time points from the reference models are listed in Supplemental Tables 3  and 4.

Kidneys
For both reference models, 48 h after injection was found to be the optimum imaging time point (Figs.1A and 1B).STP mono and STP H showed the smallest mean absolute deviations from the monoexponential reference model MTP mono , at 3% 6 4% and 4% 6 4%, respectively.Compared with the biexponential reference model MTP bi , STP bi and STP J indicated the smallest mean absolute deviations of 4% 6 4% and 4% 6 5%, respectively, with a slight preference for STP bi since for 86% (vs.71%) of VOIs the renal absorbed doses deviated less than 10% from the reference (Fig. 1D).

Salivary Glands
SPECT/CT imaging at 24 h after injection in combination with STP bi resulted in the lowest mean absolute dose deviation of 4% 6 4% (all VOIs within |10|%), when compared with the bestsuited reference model, that is, MTP bi (Figs.2B and 2D).At 48 h after injection, STP bi showed the best performance as well (mean absolute deviation of 10% 6 14%, with 70% of all VOIs within |10|%) (Figs.2B and 2D).

Lesions
Larger deviations from the reference models were observed for lesions than for at-risk organs, with 48-72 h being the best-suited time point (Figs.3A and 3B).Compared with MTP mono , STP mono and STP H -both with imaging at 72 h after injection-showed a similar performance (average deviation, 8% 6 9% and 7% 6 9%, respectively, with 73% and 70% of lesions deviating less than 10% from MTP mono ) (Figs. 3A and 3C).Compared with MTP bi , similar average deviations for all 3 STP methods could be obtained (STP bi , 10% 6 13%; STP H , 16% 6 10%; and STP J , 10% 6 10%) but with use of different optimum imaging time points (72 h for STP H and STP J , 48 h for STP bi ) (Figs. 3B and 3D).

DISCUSSION
The aim of this study was to compare different STP approaches for 2 reference models and-apart from the bone marrow-the main compartments of interest during [ 177 Lu]Lu-PSMA treatment, that is, lesions, kidneys, and salivary glands.Although MTP bi could be identified as the best-suited reference model for the salivary glands, no superiority of MTP bi or MTP mono could be established for kidney and lesion dosimetry using SPECT acquisitions at 24, 48, 72, and 168 h after injection.However, absorbed dose estimates were found to be significantly different for both reference models.A higher number of image acquisitions may help to reduce the ambiguity of the optimum reference model for lesion and kidney dosimetry.Yet, the number of image acquisitions available in a clinical setting is inherently limited.For example, although the late pharmacokinetics has a significant impact on dosimetry estimates (32), image acquisitions are usually terminated, at the latest, at around 7-9 d after injection for logistic reasons and because SPECT imaging at late time points is limited by a decreasing activity concentration.Although STP dosimetry is feasible, Figures 1, 2, 3A, and 3B highlight that the error of each STP method depends on the reference MTP protocol.Thus, an uncertainty in the reference MTP protocol automatically translates into the selection of the optimum STP method.Comparability of STP dosimetry from different studies requires careful consideration of the reference protocols that were used to define the STP methodology.In this sense, the popularity of STP dosimetry also strengthens the request for standardization of clinically feasible but reliable MTP protocols.
The optimum imaging time point for renal STP dosimetry is clearly 48 h for all STP methods and both reference models.As no superiority for MTP bi or MTP mono could be proven and, thus, the underlying pharmacokinetics is not well known, STP mono and STP bi should be avoided.Thus for kidney STP dosimetry, STP H is recommended over STP J because the number of VOIs with a deviation of less than 10% is high for both MTP mono and MTP bi .Similarly, STP J with imaging at 72 h can be recommended for lesion STP dosimetry.For the salivary glands, MTB bi could be identified as the optimum reference model, with imaging at 24 h after injection and STP bi being the best choice for STP dosimetry.
The definition of a specific STP methodology is further complicated by the fact that the optimal STP dosimetry for different compartments is usually associated with different optimum imaging time points.From a clinical perspective, STP approaches should be available with similar performance for lesions and organs at risk.However, considering the results in both Figure 1 and Figure 2, compared with Figure 3, a trade-off between the accuracy of dosimetry for lesions and at-risk organs is necessary.The optimum time point is also likely to depend on the question of whether the COMPARISON OF SINGLE-TIME-POINT DOSIMETRY Resch et al.
primary objective of dosimetry is safety or efficacy.It may be possible to merge STP dosimetry for lesions, kidneys, and salivary glands based on imaging at 48 h after therapy, although this will result in a lower level of accuracy for lesions (optimum, 72 h after injection) and salivary glands (optimum, 24 h after injection).For the salivary glands with MTP bi as the optimum reference protocol, STP bi is suggested for imaging at 48 h after injection.For lesion dosimetry, STP J is recommended for imaging at 48 h after injection, as it shows a more balanced performance for MTP bi and MTP mono than does STP H .
The overall number of patients in this study was low.Especially, the used biexponential reference model applies a population-based shared parameter g that should be reevaluated for a larger patient cohort.Further, this population-based parameter may vary over the course of subsequent therapy cycles, whereas only the first therapy cycle was investigated in this study.However, Hardiansyah et al. found a value of 0.963 6 0.004 for the renal biokinetics of 13 [ 177 Lu]Lu-PSMA-I&T patients (29), compared with a very similar value of 0.956 6 0.007 (CV, 0.7%) for 14 kidneys and 7 patients in this study (0.8% deviation).In addition, the method proposed by H€ anscheid et al. (12) was originally developed for monoexponential pharmacokinetics but was compared with a biexponential reference model in this study as well.However, the intention was to show the effect of an unknown ground truth model on STP methodology.For example, for the salivary glands, with clearly biexponential pharmacokinetics, STP H showed poor performance.Despite the smaller patient cohort, the optimum time points proposed in this study agreed well with previously published data (10,11,13,17,18).As data with a late SPECT scan at around 7 d after injection were available for only a selected number of patients undergoing their first treatment cycle in this study, no prior information on the compartment-specific effective half-life was available, limiting this study to population-based approaches only.Brosch-Lenz et al. investigated a priorinformation approach based on the patient-specific effective half-life of the previous treatment cycle in comparison to the method proposed by H€ anscheid et al. for kidney and lesion STP dosimetry and for [ 177 Lu]Lu-PSMA-I&T therapy (10,12).The reference model was a monoexponential fit with SPECT/CT imaging at 24, 48, and 72 h after treatment.The method by H€ anscheid et al. was slightly superior for the kidneys, whereas for lesion STP dosimetry the priorinformation approach showed better performance, possibly because the lesion pharmacokinetics usually shows a larger interpatient and intrapatient variability.
Population-based approaches assume an average patient with average pharmacokinetics.It should be further investigated whether patient-specific factors, such as changes in tumor volume, kidney function, or any other patient-specific factors that deviate from the average patient, may guide the decision between MTP and STP dosimetry.Scheduling MTP dosimetry intermittently (e.g., alternating between MTP and STP dosimetry) may be a trade-off between clinical efficiency and accuracy.Further, in view of the observed outliers for different STP approaches, quality control is an important aspect of STP dosimetry.The use of mixed-linear-effects models, which consider each parameter as a combination of a mixed population-based effect and a random patient-specific effect, has already been shown to be promising for reducing outliers within STP dosimetry (19,24).
Current research also focuses on speeding the SPECT acquisition, a development that is lately being driven by the integration of artificial intelligence into molecular imaging (33)(34)(35).This should be considered as an opportunity to maintain MTP-based protocols, at least in centers that hospitalize patients or where multiple examinations are feasible on an outpatient basis.

CONCLUSION
STP dosimetry is becoming more popular because it allows for efficient integration of internal dosimetry into clinical routine.Usually, however, the considered reference MTP protocol already approximates the real but unknown clinical ground truth, and its error is in addition to the error of STP dosimetry itself.The intercomparison of different STP methods shows a different optimum time point and error depending on the compartment and the reference MTP protocol.According to our patient cohort, 48 h after injection may be regarded as a compromise for STP dosimetry for lesions and at-risk organs.5 and 6. p.i. 5 after injection.5 and 6. p.i. 5 after injection.

FIGURE 1 .
FIGURE 1. (A and B) Deviation of kidney STP dosimetry from MTP dosimetry using monoexponential (A) or biexponential (B) MTP reference models and for different imaging time points.(C and D) Percentage of VOIs with deviation less than |10|% using monoexponential (C) or biexponential (D) MTP reference models and for different imaging time points.Numbers above each bar indicate exact percentages.For better visualization, data for 168 h after injection are shown in Supplemental Figure 6 and Supplemental Tables5 and 6. p.i. 5 after injection.

FIGURE 2 .
FIGURE 2. (A and B) Deviations of salivary gland STP dosimetry from MTP dosimetry using monoexponential (A) and biexponential (B) reference models and different imaging time points.(C and D) Percentage of VOIs with deviation less than |10|% using monoexponential (C) and biexponential (D) reference models and different imaging time points.Numbers above each bar indicate exact percentages.For better visualization, data for 168 h after injection are shown in Supplemental Figure6and Supplemental Tables5 and 6. p.i. 5 after injection.

FIGURE 3 .
FIGURE 3. (A and B) Deviation of lesion STP dosimetry from MTP dosimetry using monoexponential (A) or biexponential (B) MTP reference models and for different imaging time points.(C and D) Percentage of VOIs with deviation less than |10|% using monoexponential (C) or biexponential (D) MTP reference models and for different imaging time points.Numbers above each bar indicate exact percentages.For better visualization, data for 168 h after injection are shown in Supplemental Figure 6 and Supplemental Tables5 and 6. p.i. 5 after injection.

TABLE 2
Patient Information

TABLE 3
Fit and Dosimetry Results for Reference Models Wilcoxon signed-rank test.CV A /CV l 5 CV A 0 /CV l bio ; AD 6 SD 5 average deviation 6 SD of absorbed dose; SSE 5 sum of squared errors.